Aircraft: MD-11
Phase of flight: Final Approach
Anomaly: Aircraft Equipment Problem Less Severe; Deviation - Altitude Excursion From Assigned Altitude; Deviation - Altitude Crossing Restriction Not Met; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance

We were cleared for an RNAV approach. First Officer was pilot flying while the Captain was pilot not flying. Weather was VMC below 5;000 FT AGL. Horizontal visibility was unlimited. We called the field visually at least 15 miles away. We were leveled off at 1;600 FT 5 miles prior to the FAF. We were hooked up to the autopilot and in NAV and PROF. He entered in the RNAV minimums of 660 FT on the FCP as we were on the approach phase. I reminded the Captain about the .3 RNP on the REF page and he then entered it in. Almost immediately; the aircraft started a descent while we were yet 2 miles prior to the FAF. We all were aware of the deviation; caught and corrected it after a descent of approximately 400 FT. The pilot flying corrected to 1;550 FT MSL acquired the VASI and manually flew the approach visually. When on the early descent; the Controller transmitted to us to 'check our altimeter setting and altitude.' We responded that we were correcting and that we were under control. As we were in visual conditions and on a visual approach backed up by the RNAV and as the Controller asked only if we would check our instruments; we thought that we were safe from any type of ATC deviation issues. At no time were we unsafe in our approach. At no time did the Controller use the pilot deviation notification procedures as outlined in the FAA Regulations under provisions of paragraph 2-1-26 of the ATC manual asking us to contact the FAA. I was flying pilot on an RNAV approach. Per approach descended from 2;000 to 1;600. Just prior to FAF R/O prompted 0.3 for the FMS setup. It had been forgotten even though the RNP was showing far less than this value. This was a definite distraction. The aircraft descended as though on path but by 1;200 I took notice of this; disconnected autopilot and initiated a level off. Lowest about 1;100 MSL. About this time Tower issued an altitude alert; response was yes; correcting. Re Intercepted glidepath visually from about 1;300 FT with the PAPI; and continued with the approach; stable at 1;000 MSL. Had to ignore commands from Flight Director which was still commanding a descent that would have been well short. Normal landing and taxi in. Crew dispersed; I went to hotel; [and] other crew went home. Captain telephoned me later and we discussed whether to file a report. I did not feel we had violated FAR's; and if anything the system had worked as it was supposed to: to issue a timely warning. The crew response was already in action at the time of the warning. So didn't file at that time. Fatigue was a factor delaying reaction possibly. I had been woken from a planned afternoon nap by the maid attempting to clean. Do Not Disturb was ON. This happens more often than one would think; even with Do Not Disturb signs on. Worldwide; staff doesn't get the off hours and off pattern sleep habits this job requires. MD11 flight crew reports descending below the FAF altitude after altitude capture with autopilot engaged; when the MDA is set in the FCP window. The aircraft descends 400 FT before climbing back and ATC takes notice.